Stress pulse in bar with neck or swell

Summary

The transmission and reflection of an elastic rectangular stress pulse in a bar with a cylindrical neck or swell of varying length is investigated. For some cases strain-time oscillograms have been taken, which agree fairly well -with corresponding theoretical curves. These are constructed graphically through a modified form of the “graphodynamics” introduced by Bergeron and DeJuhasz, using force-velocity diagrams to obtain force-time, stram-(stress-)time, and displacement-time diagrams. The theory shows that the transmitted pulse has exactly the same shape for a neck and a swell of the same length, provided their areas satisfy a certain condition. Furthermore, the character of the event is changed at a certain length ratio between pulse and neck (swell). For shorter pulses there is no longer transmitted (reflected) one pulse, but a series of pulses of decreasing magnitudes.